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New York (CNN)President Barack Obama worked to calm Americans' jitters Monday after a series of attempts at mass violence, suggesting that yielding to fear amounted to a win for terrorists.

During two appearances in New York, Obama praised the swift work of law enforcement authorities looking into duel bomb attacks in New York and New Jersey over the weekend. And he urged Americans to follow the lead of residents here by not submitting to fear.

"I think it is important to remember what terrorists and violent extremists are trying to do. They are trying to hurt innocent people, but they also want to inspire fear in all of us, and disrupt the way we live to undermine our values," Obama said. "We all have a role to play as citizens in making sure that we don't succumb to that fear. And there is no better example of that than the people of New York and New Jersey."

"Folks around here, you know, they don't get scared. They are tough, they are resilient, they go about their business every single day. And that kind of toughness and resoluteness and a recognition that neither individuals nor organizations like ISIL can ultimately undermine our way of life," Obama said. "That's the kind of strength that makes me so proud to be an American."

The President was speaking Monday morning from a hotel in midtown Manhattan, where he's attending his final United Nations General Assembly meeting. Two miles south, in Chelsea, investigations were still piecing together evidence following a bomb explosion in a dumpster Saturday night, which injured dozens.

The attack appeared linked to another explosion in Seaside Park, New Jersey, and a series of pipe bombs found in a backpack Sunday night in Elizabeth, New Jersey. A third incident in Minnesota, where a man stabbed nine people before being shot, is being investigated separately as a "potential act of terrorism," Obama said.

Monday afternoon, Obama said he'd spoken with law enforcement officers who helped apprehend Ahmad Khan Rahami, a suspect in this weekend's bomb attacks in New York and New Jersey, and hailed their actions as heroic. He also said he phoned an off-duty officer who neutralized the attacker in Minnesota.

"It's just one more reminder of the skill and sacrifice and what they put on the line every single day to make sure we're safe," Obama said following talks with Iraq's prime minister Haider al-Abadi.

An ISIS wing claimed responsibility for the Minnesota attack, though Obama avoided pinning any specific motivation on the attacks during his appearances on Monday. He did, however, insist his administration was going after the terror group aggressively to prevent any further violence.

"We will continue to lead the global coalition on the fight to destroy ISIL, which is instigating a lot of people over the internet, to carry out attacks," Obama said, using the administration's term for the Islamic State group. "We are going to continue to go after them. We're going to take out their leaders, we're going to take out their infrastructure."

Following his talks with Abadi, Obama conceded retaking Iraq's second largest city from the terror group would be difficult.

"This is going to be challenging," Obama said of long-held plans to liberate Mosul. "We feel confident that we will be in a position to move forward fairly rapidly."

"It will be a tough fight...This is going to be hard, this is going to be challenging," Obama continued, adding he would support and assistance from other countries and from US lawmakers.